Well-posedness for one-dimensional derivative nonlinear Schrödinger equations

Chengchun Hao

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arXiv · 0811.4222

Well-posedness for one-dimensional derivative nonlinear Schrödinger equations

Chengchun Hao

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Abstract

In this paper, we investigate the one-dimensional derivative nonlinear Schrödinger equations of the form $iu_t-u_{xx}+iλ\abs{u}^k u_x=0$ with non-zero $λ\in \Real$ and any real number $k\gs 5$. We establish the local well-posedness of the Cauchy problem with any initial data in $H^{1/2}$ by using the gauge transformation and the Littlewood-Paley decomposition.

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Chengchun Hao. 2008-11-26. Well-posedness for one-dimensional derivative nonlinear Schrödinger equations. https://arxiv.org/abs/0811.4222

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